TY - JOUR

T1 - Camera-pose estimation via projective newton optimization on the manifold

AU - Sarkis, Michel

AU - Diepold, Klaus

N1 - Funding Information:
Manuscript received September 15, 2010; revised May 03, 2011, August 18, 2011, and October 10, 2011; accepted November 05, 2011. Date of publication December 02, 2011; date of current version March 21, 2012. This work was supported in part by the German Research Foundation within the Collaborative Research Center SFB 453 on “High-Fidelity Telepresence and Teleaction.” The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Jenq-Neng Hwang.

PY - 2012/4

Y1 - 2012/4

N2 - Determining the pose of a moving camera is an important task in computer vision. In this paper, we derive a projective Newton algorithm on the manifold to refine the pose estimate of a camera. The main idea is to benefit from the fact that the 3-D rigid motion is described by the special Euclidean group, which is a Riemannian manifold. The latter is equipped with a tangent space defined by the corresponding Lie algebra. This enables us to compute the optimization direction, i.e., the gradient and the Hessian, at each iteration of the projective Newton scheme on the tangent space of the manifold. Then, the motion is updated by projecting back the variables on the manifold itself. We also derive another version of the algorithm that employs homeomorphic parameterization to the special Euclidean group. We test the algorithm on several simulated and real image data sets. Compared with the standard Newton minimization scheme, we are now able to obtain the full numerical formula of the Hessian with a 60% decrease in computational complexity. Compared with Levenberg-Marquardt, the results obtained are more accurate while having a rather similar complexity.

AB - Determining the pose of a moving camera is an important task in computer vision. In this paper, we derive a projective Newton algorithm on the manifold to refine the pose estimate of a camera. The main idea is to benefit from the fact that the 3-D rigid motion is described by the special Euclidean group, which is a Riemannian manifold. The latter is equipped with a tangent space defined by the corresponding Lie algebra. This enables us to compute the optimization direction, i.e., the gradient and the Hessian, at each iteration of the projective Newton scheme on the tangent space of the manifold. Then, the motion is updated by projecting back the variables on the manifold itself. We also derive another version of the algorithm that employs homeomorphic parameterization to the special Euclidean group. We test the algorithm on several simulated and real image data sets. Compared with the standard Newton minimization scheme, we are now able to obtain the full numerical formula of the Hessian with a 60% decrease in computational complexity. Compared with Levenberg-Marquardt, the results obtained are more accurate while having a rather similar complexity.

KW - Differential geometry

KW - Newton method

KW - Riemannian manifold

KW - pose estimation

UR - http://www.scopus.com/inward/record.url?scp=84859010765&partnerID=8YFLogxK

U2 - 10.1109/TIP.2011.2177845

DO - 10.1109/TIP.2011.2177845

M3 - Article

C2 - 22155953

AN - SCOPUS:84859010765

SN - 1057-7149

VL - 21

SP - 1729

EP - 1741

JO - IEEE Transactions on Image Processing

JF - IEEE Transactions on Image Processing

IS - 4

M1 - 6094213

ER -